Problem: What do the following two equations represent? $-x-5y = 1$ $10x-2y = -5$
Putting the first equation in $y = mx + b$ form gives: $-x-5y = 1$ $-5y = x+1$ $y = -\dfrac{1}{5}x - \dfrac{1}{5}$ Putting the second equation in $y = mx + b$ form gives: $10x-2y = -5$ $-2y = -10x-5$ $y = 5x + \dfrac{5}{2}$ The slopes are negative inverses of each other, so the lines are perpendicular.